Q: What are the factor combinations of the number 812,735?

 A:
Positive:   1 x 8127355 x 1625477 x 11610511 x 7388535 x 2322155 x 1477777 x 10555385 x 2111
Negative: -1 x -812735-5 x -162547-7 x -116105-11 x -73885-35 x -23221-55 x -14777-77 x -10555-385 x -2111


How do I find the factor combinations of the number 812,735?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 812,735, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 812,735
-1 -812,735

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 812,735.

Example:
1 x 812,735 = 812,735
and
-1 x -812,735 = 812,735
Notice both answers equal 812,735

With that explanation out of the way, let's continue. Next, we take the number 812,735 and divide it by 2:

812,735 ÷ 2 = 406,367.5

If the quotient is a whole number, then 2 and 406,367.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 812,735
-1 -812,735

Now, we try dividing 812,735 by 3:

812,735 ÷ 3 = 270,911.6667

If the quotient is a whole number, then 3 and 270,911.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 812,735
-1 -812,735

Let's try dividing by 4:

812,735 ÷ 4 = 203,183.75

If the quotient is a whole number, then 4 and 203,183.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 812,735
-1 812,735
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

157113555773852,11110,55514,77723,22173,885116,105162,547812,735
-1-5-7-11-35-55-77-385-2,111-10,555-14,777-23,221-73,885-116,105-162,547-812,735

More Examples

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